Another comment mentioned the HDMI2USB project, and the main FPGA target of that project uses DDR3 FWIW. I get the impression that managing RAM is just really really really _unbelievably_ hard; not impossible, just pɹɐɥ ʎllɐǝɹ ʎllɐǝɹ.
I don't think it's that bad. Board design is, but if you are working with some standard board, say from Opal Kelly (no affiliation), then you don't have to worry about that.
But what about the DRM with HDMI? I have no idea how it works, but I assumed the signal was encrypted.